%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : KLE053+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:44:13 AM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn 5 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A,
file('theBenchmark.p',multiplicative_left_identity) ).
fof(domain2,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('theBenchmark.p',domain2) ).
fof(goals,conjecture,
! [X0] : domain(domain(X0)) = domain(X0),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] : domain(domain(X0)) = domain(X0),
inference(assume_negation,[status(cth)],[goals]) ).
fof(nnf_17,plain,
? [X0] : domain(domain(X0)) != domain(X0),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
domain(domain(sK0)) != domain(sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_17]) ).
cnf(c_20,negated_conjecture,
domain(domain(sK0)) != domain(sK0),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_24,plain,
domain(multiplication(A,domain(B))) = domain(multiplication(A,B)),
inference(clausify,[status(thm)],[domain2]) ).
cnf(c_33,plain,
multiplication(one,A) = A,
inference(clausify,[status(thm)],[multiplicative_left_identity]) ).
cnf(c_56,plain,
domain(domain(A)) = domain(multiplication(one,A)),
inference(paramod,[status(thm)],[c_33,c_24]) ).
cnf(c_54,plain,
domain(domain(A)) = domain(A),
inference(paramod,[status(thm)],[c_33,c_56]) ).
cnf(c_55,plain,
$false,
inference(resolve,[status(thm)],[c_54,c_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE053+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n017.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 19:14:17 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 2933478 was started by sandbox on n017,
% 0.18/0.44 % Fri Sep 25 19:14:17 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.47
% 0.18/0.47 % SZS status Theorem for theBenchmark
% 0.18/0.47
% 0.18/0.47 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.18/0.47 % Length of proof is 8.
% 0.18/0.47 % Level of proof is 3.
% 0.18/0.47 % Maximum clause weight is 10.000.
% 0.18/0.47 % Given clauses 10.
% 0.18/0.47
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------